- #1
Bill_Nye_Fan
- 31
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Homework Statement
A function of y, ##f(y)##, is known to be equal to the second derivative of function ##y(x)##. ( i.e. ##\frac{d^2y}{dx^2}=f\left(y\right)## )
Given that ##\int _{ }^{ }f\left(y\right)dy=x-1##, and function ##y(x)## has a stationary point at ##x=1## and an x-intercept at ##x=2##, find ##y(x)## and hence find ##f(y)##
Homework Equations
Knowledge of solving differential equations.
The Attempt at a Solution
##\int _{ }^{ }f\left(y\right)dy=x-1##
##\frac{d^2y}{dx^2}=f\left(y\right)##
##∴ \int _{ }^{ }\frac{d^2y}{dx^2}dy=\int _{ }^{ }\frac{d\left(\frac{dy}{dx}\right)}{dx}dy=x-1##
I derived both sides with respect to ##y##
##\frac{d\left(\frac{dy}{dx}\right)}{dx}=\frac{d\left(x-1\right)}{dy}##
And this is where I get stuck. I'm not sure what to do from here, can someone please help? Thank you.